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Properties

Label 4017.2.a.a.1.1
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +2.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} +4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.00000 q^{14} -2.00000 q^{15} -1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} +2.00000 q^{21} -4.00000 q^{22} +6.00000 q^{23} -3.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.00000 q^{28} +6.00000 q^{29} +2.00000 q^{30} -5.00000 q^{32} -4.00000 q^{33} +6.00000 q^{34} -4.00000 q^{35} -1.00000 q^{36} -8.00000 q^{37} +2.00000 q^{38} +1.00000 q^{39} +6.00000 q^{40} +6.00000 q^{41} -2.00000 q^{42} -12.0000 q^{43} -4.00000 q^{44} +2.00000 q^{45} -6.00000 q^{46} +1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} +6.00000 q^{51} +1.00000 q^{52} +1.00000 q^{54} +8.00000 q^{55} -6.00000 q^{56} +2.00000 q^{57} -6.00000 q^{58} +8.00000 q^{59} +2.00000 q^{60} -2.00000 q^{61} -2.00000 q^{63} +7.00000 q^{64} -2.00000 q^{65} +4.00000 q^{66} -4.00000 q^{67} +6.00000 q^{68} -6.00000 q^{69} +4.00000 q^{70} +3.00000 q^{72} -4.00000 q^{73} +8.00000 q^{74} +1.00000 q^{75} +2.00000 q^{76} -8.00000 q^{77} -1.00000 q^{78} -2.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +4.00000 q^{83} -2.00000 q^{84} -12.0000 q^{85} +12.0000 q^{86} -6.00000 q^{87} +12.0000 q^{88} +6.00000 q^{89} -2.00000 q^{90} +2.00000 q^{91} -6.00000 q^{92} -4.00000 q^{95} +5.00000 q^{96} -14.0000 q^{97} +3.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 − 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 2.00000 0.894427 0.447214 − 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.00000 −0.755929 −0.377964 − 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) −2.00000 −0.632456
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350
\(14\) 2.00000 0.534522
\(15\) −2.00000 −0.516398
\(16\) −1.00000 −0.250000
\(17\) −6.00000 −1.45521 −0.727607 − 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.00000 −0.458831 −0.229416 − 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −2.00000 −0.447214
\(21\) 2.00000 0.436436
\(22\) −4.00000 −0.852803
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −3.00000 −0.612372
\(25\) −1.00000 −0.200000
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) 2.00000 0.377964
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 2.00000 0.365148
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −5.00000 −0.883883
\(33\) −4.00000 −0.696311
\(34\) 6.00000 1.02899
\(35\) −4.00000 −0.676123
\(36\) −1.00000 −0.166667
\(37\) −8.00000 −1.31519 −0.657596 − 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 2.00000 0.324443
\(39\) 1.00000 0.160128
\(40\) 6.00000 0.948683
\(41\) 6.00000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −2.00000 −0.308607
\(43\) −12.0000 −1.82998 −0.914991 − 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) −4.00000 −0.603023
\(45\) 2.00000 0.298142
\(46\) −6.00000 −0.884652
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) 1.00000 0.141421
\(51\) 6.00000 0.840168
\(52\) 1.00000 0.138675
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 1.00000 0.136083
\(55\) 8.00000 1.07872
\(56\) −6.00000 −0.801784
\(57\) 2.00000 0.264906
\(58\) −6.00000 −0.787839
\(59\) 8.00000 1.04151 0.520756 − 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 2.00000 0.258199
\(61\) −2.00000 −0.256074 −0.128037 − 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 7.00000 0.875000
\(65\) −2.00000 −0.248069
\(66\) 4.00000 0.492366
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 6.00000 0.727607
\(69\) −6.00000 −0.722315
\(70\) 4.00000 0.478091
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 3.00000 0.353553
\(73\) −4.00000 −0.468165 −0.234082 − 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 8.00000 0.929981
\(75\) 1.00000 0.115470
\(76\) 2.00000 0.229416
\(77\) −8.00000 −0.911685
\(78\) −1.00000 −0.113228
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −2.00000 −0.223607
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) −2.00000 −0.218218
\(85\) −12.0000 −1.30158
\(86\) 12.0000 1.29399
\(87\) −6.00000 −0.643268
\(88\) 12.0000 1.27920
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −2.00000 −0.210819
\(91\) 2.00000 0.209657
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 5.00000 0.510310
\(97\) −14.0000 −1.42148 −0.710742 − 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 3.00000 0.303046
\(99\) 4.00000 0.402015
\(100\) 1.00000 0.100000
\(101\) 8.00000 0.796030 0.398015 − 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) −6.00000 −0.594089
\(103\) −1.00000 −0.0985329
\(104\) −3.00000 −0.294174
\(105\) 4.00000 0.390360
\(106\) 0 0
\(107\) 2.00000 0.193347 0.0966736 − 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) 1.00000 0.0962250
\(109\) 16.0000 1.53252 0.766261 − 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) −8.00000 −0.762770
\(111\) 8.00000 0.759326
\(112\) 2.00000 0.188982
\(113\) 4.00000 0.376288 0.188144 − 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) −2.00000 −0.187317
\(115\) 12.0000 1.11901
\(116\) −6.00000 −0.557086
\(117\) −1.00000 −0.0924500
\(118\) −8.00000 −0.736460
\(119\) 12.0000 1.10004
\(120\) −6.00000 −0.547723
\(121\) 5.00000 0.454545
\(122\) 2.00000 0.181071
\(123\) −6.00000 −0.541002
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 2.00000 0.178174
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 3.00000 0.265165
\(129\) 12.0000 1.05654
\(130\) 2.00000 0.175412
\(131\) −18.0000 −1.57267 −0.786334 − 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 4.00000 0.348155
\(133\) 4.00000 0.346844
\(134\) 4.00000 0.345547
\(135\) −2.00000 −0.172133
\(136\) −18.0000 −1.54349
\(137\) 14.0000 1.19610 0.598050 − 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 6.00000 0.510754
\(139\) 20.0000 1.69638 0.848189 − 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 4.00000 0.338062
\(141\) 0 0
\(142\) 0 0
\(143\) −4.00000 −0.334497
\(144\) −1.00000 −0.0833333
\(145\) 12.0000 0.996546
\(146\) 4.00000 0.331042
\(147\) 3.00000 0.247436
\(148\) 8.00000 0.657596
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −20.0000 −1.62758 −0.813788 − 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) −6.00000 −0.486664
\(153\) −6.00000 −0.485071
\(154\) 8.00000 0.644658
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 10.0000 0.798087 0.399043 − 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −10.0000 −0.790569
\(161\) −12.0000 −0.945732
\(162\) −1.00000 −0.0785674
\(163\) −10.0000 −0.783260 −0.391630 − 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −6.00000 −0.468521
\(165\) −8.00000 −0.622799
\(166\) −4.00000 −0.310460
\(167\) −12.0000 −0.928588 −0.464294 − 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 6.00000 0.462910
\(169\) 1.00000 0.0769231
\(170\) 12.0000 0.920358
\(171\) −2.00000 −0.152944
\(172\) 12.0000 0.914991
\(173\) 12.0000 0.912343 0.456172 − 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) 6.00000 0.454859
\(175\) 2.00000 0.151186
\(176\) −4.00000 −0.301511
\(177\) −8.00000 −0.601317
\(178\) −6.00000 −0.449719
\(179\) −26.0000 −1.94333 −0.971666 − 0.236360i \(-0.924046\pi\)
−0.971666 + 0.236360i \(0.924046\pi\)
\(180\) −2.00000 −0.149071
\(181\) −6.00000 −0.445976 −0.222988 − 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) −2.00000 −0.148250
\(183\) 2.00000 0.147844
\(184\) 18.0000 1.32698
\(185\) −16.0000 −1.17634
\(186\) 0 0
\(187\) −24.0000 −1.75505
\(188\) 0 0
\(189\) 2.00000 0.145479
\(190\) 4.00000 0.290191
\(191\) −8.00000 −0.578860 −0.289430 − 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −7.00000 −0.505181
\(193\) −4.00000 −0.287926 −0.143963 − 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 14.0000 1.00514
\(195\) 2.00000 0.143223
\(196\) 3.00000 0.214286
\(197\) −22.0000 −1.56744 −0.783718 − 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) −4.00000 −0.284268
\(199\) −8.00000 −0.567105 −0.283552 − 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) −3.00000 −0.212132
\(201\) 4.00000 0.282138
\(202\) −8.00000 −0.562878
\(203\) −12.0000 −0.842235
\(204\) −6.00000 −0.420084
\(205\) 12.0000 0.838116
\(206\) 1.00000 0.0696733
\(207\) 6.00000 0.417029
\(208\) 1.00000 0.0693375
\(209\) −8.00000 −0.553372
\(210\) −4.00000 −0.276026
\(211\) 4.00000 0.275371 0.137686 − 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.00000 −0.136717
\(215\) −24.0000 −1.63679
\(216\) −3.00000 −0.204124
\(217\) 0 0
\(218\) −16.0000 −1.08366
\(219\) 4.00000 0.270295
\(220\) −8.00000 −0.539360
\(221\) 6.00000 0.403604
\(222\) −8.00000 −0.536925
\(223\) −26.0000 −1.74109 −0.870544 − 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 10.0000 0.668153
\(225\) −1.00000 −0.0666667
\(226\) −4.00000 −0.266076
\(227\) 4.00000 0.265489 0.132745 − 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) −2.00000 −0.132453
\(229\) −22.0000 −1.45380 −0.726900 − 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) −12.0000 −0.791257
\(231\) 8.00000 0.526361
\(232\) 18.0000 1.18176
\(233\) 4.00000 0.262049 0.131024 − 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 1.00000 0.0653720
\(235\) 0 0
\(236\) −8.00000 −0.520756
\(237\) 0 0
\(238\) −12.0000 −0.777844
\(239\) −20.0000 −1.29369 −0.646846 − 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 2.00000 0.129099
\(241\) 8.00000 0.515325 0.257663 − 0.966235i \(-0.417048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) −5.00000 −0.321412
\(243\) −1.00000 −0.0641500
\(244\) 2.00000 0.128037
\(245\) −6.00000 −0.383326
\(246\) 6.00000 0.382546
\(247\) 2.00000 0.127257
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 12.0000 0.758947
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 2.00000 0.125988
\(253\) 24.0000 1.50887
\(254\) 0 0
\(255\) 12.0000 0.751469
\(256\) −17.0000 −1.06250
\(257\) −8.00000 −0.499026 −0.249513 − 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) −12.0000 −0.747087
\(259\) 16.0000 0.994192
\(260\) 2.00000 0.124035
\(261\) 6.00000 0.371391
\(262\) 18.0000 1.11204
\(263\) 4.00000 0.246651 0.123325 − 0.992366i \(-0.460644\pi\)
0.123325 + 0.992366i \(0.460644\pi\)
\(264\) −12.0000 −0.738549
\(265\) 0 0
\(266\) −4.00000 −0.245256
\(267\) −6.00000 −0.367194
\(268\) 4.00000 0.244339
\(269\) 10.0000 0.609711 0.304855 − 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 2.00000 0.121716
\(271\) −8.00000 −0.485965 −0.242983 − 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 6.00000 0.363803
\(273\) −2.00000 −0.121046
\(274\) −14.0000 −0.845771
\(275\) −4.00000 −0.241209
\(276\) 6.00000 0.361158
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −20.0000 −1.19952
\(279\) 0 0
\(280\) −12.0000 −0.717137
\(281\) −30.0000 −1.78965 −0.894825 − 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) 4.00000 0.236940
\(286\) 4.00000 0.236525
\(287\) −12.0000 −0.708338
\(288\) −5.00000 −0.294628
\(289\) 19.0000 1.11765
\(290\) −12.0000 −0.704664
\(291\) 14.0000 0.820695
\(292\) 4.00000 0.234082
\(293\) −18.0000 −1.05157 −0.525786 − 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) −3.00000 −0.174964
\(295\) 16.0000 0.931556
\(296\) −24.0000 −1.39497
\(297\) −4.00000 −0.232104
\(298\) −6.00000 −0.347571
\(299\) −6.00000 −0.346989
\(300\) −1.00000 −0.0577350
\(301\) 24.0000 1.38334
\(302\) 20.0000 1.15087
\(303\) −8.00000 −0.459588
\(304\) 2.00000 0.114708
\(305\) −4.00000 −0.229039
\(306\) 6.00000 0.342997
\(307\) −16.0000 −0.913168 −0.456584 − 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 8.00000 0.455842
\(309\) 1.00000 0.0568880
\(310\) 0 0
\(311\) 14.0000 0.793867 0.396934 − 0.917847i \(-0.370074\pi\)
0.396934 + 0.917847i \(0.370074\pi\)
\(312\) 3.00000 0.169842
\(313\) 10.0000 0.565233 0.282617 − 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) −10.0000 −0.564333
\(315\) −4.00000 −0.225374
\(316\) 0 0
\(317\) 2.00000 0.112331 0.0561656 − 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 0 0
\(319\) 24.0000 1.34374
\(320\) 14.0000 0.782624
\(321\) −2.00000 −0.111629
\(322\) 12.0000 0.668734
\(323\) 12.0000 0.667698
\(324\) −1.00000 −0.0555556
\(325\) 1.00000 0.0554700
\(326\) 10.0000 0.553849
\(327\) −16.0000 −0.884802
\(328\) 18.0000 0.993884
\(329\) 0 0
\(330\) 8.00000 0.440386
\(331\) −20.0000 −1.09930 −0.549650 − 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) −4.00000 −0.219529
\(333\) −8.00000 −0.438397
\(334\) 12.0000 0.656611
\(335\) −8.00000 −0.437087
\(336\) −2.00000 −0.109109
\(337\) 2.00000 0.108947 0.0544735 − 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −4.00000 −0.217250
\(340\) 12.0000 0.650791
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) 20.0000 1.07990
\(344\) −36.0000 −1.94099
\(345\) −12.0000 −0.646058
\(346\) −12.0000 −0.645124
\(347\) −22.0000 −1.18102 −0.590511 − 0.807030i \(-0.701074\pi\)
−0.590511 + 0.807030i \(0.701074\pi\)
\(348\) 6.00000 0.321634
\(349\) 16.0000 0.856460 0.428230 − 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) −2.00000 −0.106904
\(351\) 1.00000 0.0533761
\(352\) −20.0000 −1.06600
\(353\) −6.00000 −0.319348 −0.159674 − 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 8.00000 0.425195
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −12.0000 −0.635107
\(358\) 26.0000 1.37414
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 6.00000 0.316228
\(361\) −15.0000 −0.789474
\(362\) 6.00000 0.315353
\(363\) −5.00000 −0.262432
\(364\) −2.00000 −0.104828
\(365\) −8.00000 −0.418739
\(366\) −2.00000 −0.104542
\(367\) −8.00000 −0.417597 −0.208798 − 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) −6.00000 −0.312772
\(369\) 6.00000 0.312348
\(370\) 16.0000 0.831800
\(371\) 0 0
\(372\) 0 0
\(373\) 10.0000 0.517780 0.258890 − 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 24.0000 1.24101
\(375\) 12.0000 0.619677
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) −2.00000 −0.102869
\(379\) −24.0000 −1.23280 −0.616399 − 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 4.00000 0.205196
\(381\) 0 0
\(382\) 8.00000 0.409316
\(383\) 24.0000 1.22634 0.613171 − 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) −3.00000 −0.153093
\(385\) −16.0000 −0.815436
\(386\) 4.00000 0.203595
\(387\) −12.0000 −0.609994
\(388\) 14.0000 0.710742
\(389\) −4.00000 −0.202808 −0.101404 − 0.994845i \(-0.532333\pi\)
−0.101404 + 0.994845i \(0.532333\pi\)
\(390\) −2.00000 −0.101274
\(391\) −36.0000 −1.82060
\(392\) −9.00000 −0.454569
\(393\) 18.0000 0.907980
\(394\) 22.0000 1.10834
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) −4.00000 −0.200754 −0.100377 − 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 8.00000 0.401004
\(399\) −4.00000 −0.200250
\(400\) 1.00000 0.0500000
\(401\) −6.00000 −0.299626 −0.149813 − 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) −4.00000 −0.199502
\(403\) 0 0
\(404\) −8.00000 −0.398015
\(405\) 2.00000 0.0993808
\(406\) 12.0000 0.595550
\(407\) −32.0000 −1.58618
\(408\) 18.0000 0.891133
\(409\) −18.0000 −0.890043 −0.445021 − 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) −12.0000 −0.592638
\(411\) −14.0000 −0.690569
\(412\) 1.00000 0.0492665
\(413\) −16.0000 −0.787309
\(414\) −6.00000 −0.294884
\(415\) 8.00000 0.392705
\(416\) 5.00000 0.245145
\(417\) −20.0000 −0.979404
\(418\) 8.00000 0.391293
\(419\) 10.0000 0.488532 0.244266 − 0.969708i \(-0.421453\pi\)
0.244266 + 0.969708i \(0.421453\pi\)
\(420\) −4.00000 −0.195180
\(421\) −2.00000 −0.0974740 −0.0487370 − 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) −4.00000 −0.194717
\(423\) 0 0
\(424\) 0 0
\(425\) 6.00000 0.291043
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) −2.00000 −0.0966736
\(429\) 4.00000 0.193122
\(430\) 24.0000 1.15738
\(431\) 8.00000 0.385346 0.192673 − 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 1.00000 0.0481125
\(433\) −34.0000 −1.63394 −0.816968 − 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) −12.0000 −0.575356
\(436\) −16.0000 −0.766261
\(437\) −12.0000 −0.574038
\(438\) −4.00000 −0.191127
\(439\) 16.0000 0.763638 0.381819 − 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 24.0000 1.14416
\(441\) −3.00000 −0.142857
\(442\) −6.00000 −0.285391
\(443\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) −8.00000 −0.379663
\(445\) 12.0000 0.568855
\(446\) 26.0000 1.23114
\(447\) −6.00000 −0.283790
\(448\) −14.0000 −0.661438
\(449\) −18.0000 −0.849473 −0.424736 − 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 1.00000 0.0471405
\(451\) 24.0000 1.13012
\(452\) −4.00000 −0.188144
\(453\) 20.0000 0.939682
\(454\) −4.00000 −0.187729
\(455\) 4.00000 0.187523
\(456\) 6.00000 0.280976
\(457\) 28.0000 1.30978 0.654892 − 0.755722i \(-0.272714\pi\)
0.654892 + 0.755722i \(0.272714\pi\)
\(458\) 22.0000 1.02799
\(459\) 6.00000 0.280056
\(460\) −12.0000 −0.559503
\(461\) −14.0000 −0.652045 −0.326023 − 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) −8.00000 −0.372194
\(463\) 4.00000 0.185896 0.0929479 − 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −4.00000 −0.185296
\(467\) −22.0000 −1.01804 −0.509019 − 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(468\) 1.00000 0.0462250
\(469\) 8.00000 0.369406
\(470\) 0 0
\(471\) −10.0000 −0.460776
\(472\) 24.0000 1.10469
\(473\) −48.0000 −2.20704
\(474\) 0 0
\(475\) 2.00000 0.0917663
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 20.0000 0.914779
\(479\) 16.0000 0.731059 0.365529 − 0.930800i \(-0.380888\pi\)
0.365529 + 0.930800i \(0.380888\pi\)
\(480\) 10.0000 0.456435
\(481\) 8.00000 0.364769
\(482\) −8.00000 −0.364390
\(483\) 12.0000 0.546019
\(484\) −5.00000 −0.227273
\(485\) −28.0000 −1.27141
\(486\) 1.00000 0.0453609
\(487\) −16.0000 −0.725029 −0.362515 − 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −6.00000 −0.271607
\(489\) 10.0000 0.452216
\(490\) 6.00000 0.271052
\(491\) −34.0000 −1.53440 −0.767199 − 0.641409i \(-0.778350\pi\)
−0.767199 + 0.641409i \(0.778350\pi\)
\(492\) 6.00000 0.270501
\(493\) −36.0000 −1.62136
\(494\) −2.00000 −0.0899843
\(495\) 8.00000 0.359573
\(496\) 0 0
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) −20.0000 −0.895323 −0.447661 − 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 12.0000 0.536656
\(501\) 12.0000 0.536120
\(502\) 0 0
\(503\) 6.00000 0.267527 0.133763 − 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) −6.00000 −0.267261
\(505\) 16.0000 0.711991
\(506\) −24.0000 −1.06693
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −18.0000 −0.797836 −0.398918 − 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) −12.0000 −0.531369
\(511\) 8.00000 0.353899
\(512\) 11.0000 0.486136
\(513\) 2.00000 0.0883022
\(514\) 8.00000 0.352865
\(515\) −2.00000 −0.0881305
\(516\) −12.0000 −0.528271
\(517\) 0 0
\(518\) −16.0000 −0.703000
\(519\) −12.0000 −0.526742
\(520\) −6.00000 −0.263117
\(521\) 4.00000 0.175243 0.0876216 − 0.996154i \(-0.472073\pi\)
0.0876216 + 0.996154i \(0.472073\pi\)
\(522\) −6.00000 −0.262613
\(523\) −36.0000 −1.57417 −0.787085 − 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 18.0000 0.786334
\(525\) −2.00000 −0.0872872
\(526\) −4.00000 −0.174408
\(527\) 0 0
\(528\) 4.00000 0.174078
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 8.00000 0.347170
\(532\) −4.00000 −0.173422
\(533\) −6.00000 −0.259889
\(534\) 6.00000 0.259645
\(535\) 4.00000 0.172935
\(536\) −12.0000 −0.518321
\(537\) 26.0000 1.12198
\(538\) −10.0000 −0.431131
\(539\) −12.0000 −0.516877
\(540\) 2.00000 0.0860663
\(541\) 30.0000 1.28980 0.644900 − 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 8.00000 0.343629
\(543\) 6.00000 0.257485
\(544\) 30.0000 1.28624
\(545\) 32.0000 1.37073
\(546\) 2.00000 0.0855921
\(547\) −40.0000 −1.71028 −0.855138 − 0.518400i \(-0.826528\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) −14.0000 −0.598050
\(549\) −2.00000 −0.0853579
\(550\) 4.00000 0.170561
\(551\) −12.0000 −0.511217
\(552\) −18.0000 −0.766131
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 16.0000 0.679162
\(556\) −20.0000 −0.848189
\(557\) 22.0000 0.932170 0.466085 − 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) 0 0
\(559\) 12.0000 0.507546
\(560\) 4.00000 0.169031
\(561\) 24.0000 1.01328
\(562\) 30.0000 1.26547
\(563\) −24.0000 −1.01148 −0.505740 − 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) 8.00000 0.336563
\(566\) 4.00000 0.168133
\(567\) −2.00000 −0.0839921
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 − 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) −4.00000 −0.167542
\(571\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 4.00000 0.167248
\(573\) 8.00000 0.334205
\(574\) 12.0000 0.500870
\(575\) −6.00000 −0.250217
\(576\) 7.00000 0.291667
\(577\) 24.0000 0.999133 0.499567 − 0.866276i \(-0.333493\pi\)
0.499567 + 0.866276i \(0.333493\pi\)
\(578\) −19.0000 −0.790296
\(579\) 4.00000 0.166234
\(580\) −12.0000 −0.498273
\(581\) −8.00000 −0.331896
\(582\) −14.0000 −0.580319
\(583\) 0 0
\(584\) −12.0000 −0.496564
\(585\) −2.00000 −0.0826898
\(586\) 18.0000 0.743573
\(587\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) −3.00000 −0.123718
\(589\) 0 0
\(590\) −16.0000 −0.658710
\(591\) 22.0000 0.904959
\(592\) 8.00000 0.328798
\(593\) 22.0000 0.903432 0.451716 − 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) 4.00000 0.164122
\(595\) 24.0000 0.983904
\(596\) −6.00000 −0.245770
\(597\) 8.00000 0.327418
\(598\) 6.00000 0.245358
\(599\) 12.0000 0.490307 0.245153 − 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 3.00000 0.122474
\(601\) −26.0000 −1.06056 −0.530281 − 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) −24.0000 −0.978167
\(603\) −4.00000 −0.162893
\(604\) 20.0000 0.813788
\(605\) 10.0000 0.406558
\(606\) 8.00000 0.324978
\(607\) 20.0000 0.811775 0.405887 − 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 10.0000 0.405554
\(609\) 12.0000 0.486265
\(610\) 4.00000 0.161955
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) −2.00000 −0.0807792 −0.0403896 − 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 16.0000 0.645707
\(615\) −12.0000 −0.483887
\(616\) −24.0000 −0.966988
\(617\) 2.00000 0.0805170 0.0402585 − 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 14.0000 0.562708 0.281354 − 0.959604i \(-0.409217\pi\)
0.281354 + 0.959604i \(0.409217\pi\)
\(620\) 0 0
\(621\) −6.00000 −0.240772
\(622\) −14.0000 −0.561349
\(623\) −12.0000 −0.480770
\(624\) −1.00000 −0.0400320
\(625\) −19.0000 −0.760000
\(626\) −10.0000 −0.399680
\(627\) 8.00000 0.319489
\(628\) −10.0000 −0.399043
\(629\) 48.0000 1.91389
\(630\) 4.00000 0.159364
\(631\) −42.0000 −1.67199 −0.835997 − 0.548734i \(-0.815110\pi\)
−0.835997 + 0.548734i \(0.815110\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) −2.00000 −0.0794301
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 0.118864
\(638\) −24.0000 −0.950169
\(639\) 0 0
\(640\) 6.00000 0.237171
\(641\) 10.0000 0.394976 0.197488 − 0.980305i \(-0.436722\pi\)
0.197488 + 0.980305i \(0.436722\pi\)
\(642\) 2.00000 0.0789337
\(643\) −34.0000 −1.34083 −0.670415 − 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 12.0000 0.472866
\(645\) 24.0000 0.944999
\(646\) −12.0000 −0.472134
\(647\) 42.0000 1.65119 0.825595 − 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) 3.00000 0.117851
\(649\) 32.0000 1.25611
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) −8.00000 −0.313064 −0.156532 − 0.987673i \(-0.550031\pi\)
−0.156532 + 0.987673i \(0.550031\pi\)
\(654\) 16.0000 0.625650
\(655\) −36.0000 −1.40664
\(656\) −6.00000 −0.234261
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) −18.0000 −0.701180 −0.350590 − 0.936529i \(-0.614019\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(660\) 8.00000 0.311400
\(661\) 4.00000 0.155582 0.0777910 − 0.996970i \(-0.475213\pi\)
0.0777910 + 0.996970i \(0.475213\pi\)
\(662\) 20.0000 0.777322
\(663\) −6.00000 −0.233021
\(664\) 12.0000 0.465690
\(665\) 8.00000 0.310227
\(666\) 8.00000 0.309994
\(667\) 36.0000 1.39393
\(668\) 12.0000 0.464294
\(669\) 26.0000 1.00522
\(670\) 8.00000 0.309067
\(671\) −8.00000 −0.308837
\(672\) −10.0000 −0.385758
\(673\) 34.0000 1.31060 0.655302 − 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −2.00000 −0.0770371
\(675\) 1.00000 0.0384900
\(676\) −1.00000 −0.0384615
\(677\) −22.0000 −0.845529 −0.422764 − 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 4.00000 0.153619
\(679\) 28.0000 1.07454
\(680\) −36.0000 −1.38054
\(681\) −4.00000 −0.153280
\(682\) 0 0
\(683\) 44.0000 1.68361 0.841807 − 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) 2.00000 0.0764719
\(685\) 28.0000 1.06983
\(686\) −20.0000 −0.763604
\(687\) 22.0000 0.839352
\(688\) 12.0000 0.457496
\(689\) 0 0
\(690\) 12.0000 0.456832
\(691\) −12.0000 −0.456502 −0.228251 − 0.973602i \(-0.573301\pi\)
−0.228251 + 0.973602i \(0.573301\pi\)
\(692\) −12.0000 −0.456172
\(693\) −8.00000 −0.303895
\(694\) 22.0000 0.835109
\(695\) 40.0000 1.51729
\(696\) −18.0000 −0.682288
\(697\) −36.0000 −1.36360
\(698\) −16.0000 −0.605609
\(699\) −4.00000 −0.151294
\(700\) −2.00000 −0.0755929
\(701\) 46.0000 1.73740 0.868698 − 0.495342i \(-0.164957\pi\)
0.868698 + 0.495342i \(0.164957\pi\)
\(702\) −1.00000 −0.0377426
\(703\) 16.0000 0.603451
\(704\) 28.0000 1.05529
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) −16.0000 −0.601742
\(708\) 8.00000 0.300658
\(709\) −38.0000 −1.42712 −0.713560 − 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 18.0000 0.674579
\(713\) 0 0
\(714\) 12.0000 0.449089
\(715\) −8.00000 −0.299183
\(716\) 26.0000 0.971666
\(717\) 20.0000 0.746914
\(718\) 0 0
\(719\) 52.0000 1.93927 0.969636 − 0.244551i \(-0.0786406\pi\)
0.969636 + 0.244551i \(0.0786406\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 2.00000 0.0744839
\(722\) 15.0000 0.558242
\(723\) −8.00000 −0.297523
\(724\) 6.00000 0.222988
\(725\) −6.00000 −0.222834
\(726\) 5.00000 0.185567
\(727\) −48.0000 −1.78022 −0.890111 − 0.455744i \(-0.849373\pi\)
−0.890111 + 0.455744i \(0.849373\pi\)
\(728\) 6.00000 0.222375
\(729\) 1.00000 0.0370370
\(730\) 8.00000 0.296093
\(731\) 72.0000 2.66302
\(732\) −2.00000 −0.0739221
\(733\) 28.0000 1.03420 0.517102 − 0.855924i \(-0.327011\pi\)
0.517102 + 0.855924i \(0.327011\pi\)
\(734\) 8.00000 0.295285
\(735\) 6.00000 0.221313
\(736\) −30.0000 −1.10581
\(737\) −16.0000 −0.589368
\(738\) −6.00000 −0.220863
\(739\) −34.0000 −1.25071 −0.625355 − 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) 16.0000 0.588172
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 − 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 12.0000 0.439646
\(746\) −10.0000 −0.366126
\(747\) 4.00000 0.146352
\(748\) 24.0000 0.877527
\(749\) −4.00000 −0.146157
\(750\) −12.0000 −0.438178
\(751\) −4.00000 −0.145962 −0.0729810 − 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 6.00000 0.218507
\(755\) −40.0000 −1.45575
\(756\) −2.00000 −0.0727393
\(757\) 26.0000 0.944986 0.472493 − 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 24.0000 0.871719
\(759\) −24.0000 −0.871145
\(760\) −12.0000 −0.435286
\(761\) 26.0000 0.942499 0.471250 − 0.882000i \(-0.343803\pi\)
0.471250 + 0.882000i \(0.343803\pi\)
\(762\) 0 0
\(763\) −32.0000 −1.15848
\(764\) 8.00000 0.289430
\(765\) −12.0000 −0.433861
\(766\) −24.0000 −0.867155
\(767\) −8.00000 −0.288863
\(768\) 17.0000 0.613435
\(769\) 12.0000 0.432731 0.216366 − 0.976312i \(-0.430580\pi\)
0.216366 + 0.976312i \(0.430580\pi\)
\(770\) 16.0000 0.576600
\(771\) 8.00000 0.288113
\(772\) 4.00000 0.143963
\(773\) −6.00000 −0.215805 −0.107903 − 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 12.0000 0.431331
\(775\) 0 0
\(776\) −42.0000 −1.50771
\(777\) −16.0000 −0.573997
\(778\) 4.00000 0.143407
\(779\) −12.0000 −0.429945
\(780\) −2.00000 −0.0716115
\(781\) 0 0
\(782\) 36.0000 1.28736
\(783\) −6.00000 −0.214423
\(784\) 3.00000 0.107143
\(785\) 20.0000 0.713831
\(786\) −18.0000 −0.642039
\(787\) −6.00000 −0.213877 −0.106938 − 0.994266i \(-0.534105\pi\)
−0.106938 + 0.994266i \(0.534105\pi\)
\(788\) 22.0000 0.783718
\(789\) −4.00000 −0.142404
\(790\) 0 0
\(791\) −8.00000 −0.284447
\(792\) 12.0000 0.426401
\(793\) 2.00000 0.0710221
\(794\) 4.00000 0.141955
\(795\) 0 0
\(796\) 8.00000 0.283552
\(797\) −22.0000 −0.779280 −0.389640 − 0.920967i \(-0.627401\pi\)
−0.389640 + 0.920967i \(0.627401\pi\)
\(798\) 4.00000 0.141598
\(799\) 0 0
\(800\) 5.00000 0.176777
\(801\) 6.00000 0.212000
\(802\) 6.00000 0.211867
\(803\) −16.0000 −0.564628
\(804\) −4.00000 −0.141069
\(805\) −24.0000 −0.845889
\(806\) 0 0
\(807\) −10.0000 −0.352017
\(808\) 24.0000 0.844317
\(809\) −32.0000 −1.12506 −0.562530 − 0.826777i \(-0.690172\pi\)
−0.562530 + 0.826777i \(0.690172\pi\)
\(810\) −2.00000 −0.0702728
\(811\) 16.0000 0.561836 0.280918 − 0.959732i \(-0.409361\pi\)
0.280918 + 0.959732i \(0.409361\pi\)
\(812\) 12.0000 0.421117
\(813\) 8.00000 0.280572
\(814\) 32.0000 1.12160
\(815\) −20.0000 −0.700569
\(816\) −6.00000 −0.210042
\(817\) 24.0000 0.839654
\(818\) 18.0000 0.629355
\(819\) 2.00000 0.0698857
\(820\) −12.0000 −0.419058
\(821\) 38.0000 1.32621 0.663105 − 0.748527i \(-0.269238\pi\)
0.663105 + 0.748527i \(0.269238\pi\)
\(822\) 14.0000 0.488306
\(823\) −56.0000 −1.95204 −0.976019 − 0.217687i \(-0.930149\pi\)
−0.976019 + 0.217687i \(0.930149\pi\)
\(824\) −3.00000 −0.104510
\(825\) 4.00000 0.139262
\(826\) 16.0000 0.556711
\(827\) −12.0000 −0.417281 −0.208640 − 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −6.00000 −0.208514
\(829\) 14.0000 0.486240 0.243120 − 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) −8.00000 −0.277684
\(831\) 2.00000 0.0693792
\(832\) −7.00000 −0.242681
\(833\) 18.0000 0.623663
\(834\) 20.0000 0.692543
\(835\) −24.0000 −0.830554
\(836\) 8.00000 0.276686
\(837\) 0 0
\(838\) −10.0000 −0.345444
\(839\) 4.00000 0.138095 0.0690477 − 0.997613i \(-0.478004\pi\)
0.0690477 + 0.997613i \(0.478004\pi\)
\(840\) 12.0000 0.414039
\(841\) 7.00000 0.241379
\(842\) 2.00000 0.0689246
\(843\) 30.0000 1.03325
\(844\) −4.00000 −0.137686
\(845\) 2.00000 0.0688021
\(846\) 0 0
\(847\) −10.0000 −0.343604
\(848\) 0 0
\(849\) 4.00000 0.137280
\(850\) −6.00000 −0.205798
\(851\) −48.0000 −1.64542
\(852\) 0 0
\(853\) 26.0000 0.890223 0.445112 − 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) −4.00000 −0.136877
\(855\) −4.00000 −0.136797
\(856\) 6.00000 0.205076
\(857\) 30.0000 1.02478 0.512390 − 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) −4.00000 −0.136558
\(859\) −12.0000 −0.409435 −0.204717 − 0.978821i \(-0.565628\pi\)
−0.204717 + 0.978821i \(0.565628\pi\)
\(860\) 24.0000 0.818393
\(861\) 12.0000 0.408959
\(862\) −8.00000 −0.272481
\(863\) 16.0000 0.544646 0.272323 − 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) 5.00000 0.170103
\(865\) 24.0000 0.816024
\(866\) 34.0000 1.15537
\(867\) −19.0000 −0.645274
\(868\) 0 0
\(869\) 0 0
\(870\) 12.0000 0.406838
\(871\) 4.00000 0.135535
\(872\) 48.0000 1.62549
\(873\) −14.0000 −0.473828
\(874\) 12.0000 0.405906
\(875\) 24.0000 0.811348
\(876\) −4.00000 −0.135147
\(877\) −24.0000 −0.810422 −0.405211 − 0.914223i \(-0.632802\pi\)
−0.405211 + 0.914223i \(0.632802\pi\)
\(878\) −16.0000 −0.539974
\(879\) 18.0000 0.607125
\(880\) −8.00000 −0.269680
\(881\) 36.0000 1.21287 0.606435 − 0.795133i \(-0.292599\pi\)
0.606435 + 0.795133i \(0.292599\pi\)
\(882\) 3.00000 0.101015
\(883\) 16.0000 0.538443 0.269221 − 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) −6.00000 −0.201802
\(885\) −16.0000 −0.537834
\(886\) 0 0
\(887\) 34.0000 1.14161 0.570804 − 0.821086i \(-0.306632\pi\)
0.570804 + 0.821086i \(0.306632\pi\)
\(888\) 24.0000 0.805387
\(889\) 0 0
\(890\) −12.0000 −0.402241
\(891\) 4.00000 0.134005
\(892\) 26.0000 0.870544
\(893\) 0 0
\(894\) 6.00000 0.200670
\(895\) −52.0000 −1.73817
\(896\) −6.00000 −0.200446
\(897\) 6.00000 0.200334
\(898\) 18.0000 0.600668
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) −24.0000 −0.799113
\(903\) −24.0000 −0.798670
\(904\) 12.0000 0.399114
\(905\) −12.0000 −0.398893
\(906\) −20.0000 −0.664455
\(907\) −24.0000 −0.796907 −0.398453 − 0.917189i \(-0.630453\pi\)
−0.398453 + 0.917189i \(0.630453\pi\)
\(908\) −4.00000 −0.132745
\(909\) 8.00000 0.265343
\(910\) −4.00000 −0.132599
\(911\) −12.0000 −0.397578 −0.198789 − 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) −2.00000 −0.0662266
\(913\) 16.0000 0.529523
\(914\) −28.0000 −0.926158
\(915\) 4.00000 0.132236
\(916\) 22.0000 0.726900
\(917\) 36.0000 1.18882
\(918\) −6.00000 −0.198030
\(919\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 36.0000 1.18688
\(921\) 16.0000 0.527218
\(922\) 14.0000 0.461065
\(923\) 0 0
\(924\) −8.00000 −0.263181
\(925\) 8.00000 0.263038
\(926\) −4.00000 −0.131448
\(927\) −1.00000 −0.0328443
\(928\) −30.0000 −0.984798
\(929\) −10.0000 −0.328089 −0.164045 − 0.986453i \(-0.552454\pi\)
−0.164045 + 0.986453i \(0.552454\pi\)
\(930\) 0 0
\(931\) 6.00000 0.196642
\(932\) −4.00000 −0.131024
\(933\) −14.0000 −0.458339
\(934\) 22.0000 0.719862
\(935\) −48.0000 −1.56977
\(936\) −3.00000 −0.0980581
\(937\) 10.0000 0.326686 0.163343 − 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) −8.00000 −0.261209
\(939\) −10.0000 −0.326338
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 − 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 10.0000 0.325818
\(943\) 36.0000 1.17232
\(944\) −8.00000 −0.260378
\(945\) 4.00000 0.130120
\(946\) 48.0000 1.56061
\(947\) −4.00000 −0.129983 −0.0649913 − 0.997886i \(-0.520702\pi\)
−0.0649913 + 0.997886i \(0.520702\pi\)
\(948\) 0 0
\(949\) 4.00000 0.129845
\(950\) −2.00000 −0.0648886
\(951\) −2.00000 −0.0648544
\(952\) 36.0000 1.16677
\(953\) 6.00000 0.194359 0.0971795 − 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 0 0
\(955\) −16.0000 −0.517748
\(956\) 20.0000 0.646846
\(957\) −24.0000 −0.775810
\(958\) −16.0000 −0.516937
\(959\) −28.0000 −0.904167
\(960\) −14.0000 −0.451848
\(961\) −31.0000 −1.00000
\(962\) −8.00000 −0.257930
\(963\) 2.00000 0.0644491
\(964\) −8.00000 −0.257663
\(965\) −8.00000 −0.257529
\(966\) −12.0000 −0.386094
\(967\) 48.0000 1.54358 0.771788 − 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) 15.0000 0.482118
\(969\) −12.0000 −0.385496
\(970\) 28.0000 0.899026
\(971\) −4.00000 −0.128366 −0.0641831 − 0.997938i \(-0.520444\pi\)
−0.0641831 + 0.997938i \(0.520444\pi\)
\(972\) 1.00000 0.0320750
\(973\) −40.0000 −1.28234
\(974\) 16.0000 0.512673
\(975\) −1.00000 −0.0320256
\(976\) 2.00000 0.0640184
\(977\) 10.0000 0.319928 0.159964 − 0.987123i \(-0.448862\pi\)
0.159964 + 0.987123i \(0.448862\pi\)
\(978\) −10.0000 −0.319765
\(979\) 24.0000 0.767043
\(980\) 6.00000 0.191663
\(981\) 16.0000 0.510841
\(982\) 34.0000 1.08498
\(983\) 60.0000 1.91370 0.956851 − 0.290578i \(-0.0938475\pi\)
0.956851 + 0.290578i \(0.0938475\pi\)
\(984\) −18.0000 −0.573819
\(985\) −44.0000 −1.40196
\(986\) 36.0000 1.14647
\(987\) 0 0
\(988\) −2.00000 −0.0636285
\(989\) −72.0000 −2.28947
\(990\) −8.00000 −0.254257
\(991\) 4.00000 0.127064 0.0635321 − 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 0 0
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) −16.0000 −0.507234
\(996\) 4.00000 0.126745
\(997\) 30.0000 0.950110 0.475055 − 0.879956i \(-0.342428\pi\)
0.475055 + 0.879956i \(0.342428\pi\)
\(998\) 20.0000 0.633089
\(999\) 8.00000 0.253109
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4017.2.a.a.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.a.1.1 ✓ 1 1.1 even 1 trivial